One of the most promising technologies for high-speed access to the Internet are Passive Optical Networks as they provide high data rates at low cost. We integrate network coding into the Ethernet Passive Optical Network architecture to increase downlink throughput by up to 50% without changing the physical layer. In contrast to previous work, we suggest to code packets not only between pairs of nodes but also between an arbitrary number of nodes forming a cycle. We characterize the expected gain analytically and by means of simulations and investigate the trade-off between queuing delay, traffic variability, and throughput gain. We show that in practical scenarios, a simple scheme already achieves a reasonable amount of the maximum possible coding gain.